Shor算法中的虚数性资源
Imaginarity as a resource in Shor's algorithm
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中文总结 AI 辅助
本研究从量子通道虚数性角度分析Shor顺序求阶算法，发现理想情况下残余虚数性与成功概率相关，并推导了理想及有噪声情况下的成功概率界限，阐明了虚数性在量子算法中的资源作用。
中文摘要 AI 辅助
我们从量子通道的虚数性角度研究Shor顺序求阶算法的顺序版本。通过固定模乘酉算子的一个特征分支和目标输出路径，该过程被有效分解为一个实对角因子和一个残余相位通道。我们发现，对于理想的残余相位通道，三个由迹范数诱导的虚数性度量均相等。在好的输出路径上，较小的残余虚数性对应于较高的单块成功概率。通过结合分支概率，我们获得了顺序求阶协议的确切理想成功概率，并推导了以残余相位通道虚数性表示的上界和下界。我们进一步将分析扩展到有噪声的残余相位通道，并获得了有噪声成功概率的上界和下界。这些结果阐明了通道虚数性在Shor算法中的作用，并为理想和有噪声的顺序量子算法中的量子资源行为提供了精细的视角。
英文摘要
We investigate the sequential version of Shor's order-finding algorithm from the perspective of the imaginarity of quantum channels. By fixing an eigenbranch of the modular multiplication unitary and a target output path, the process is effectively decomposed into a real diagonal factor and a residual phase channel. We find that for the ideal residual phase channel, the three trace-norm induced imaginarity measures are all equal. On good output paths, a smaller residual imaginarity corresponds to a higher single-block success probability. By combining the branch-wise probabilities, we obtain the exact ideal success probability of the sequential order-finding protocol and derive lower and upper bounds in terms of residual phase-channel imaginarity. We further extend the analysis to noisy residual phase channels, and obtain the lower and upper bounds on the noisy success probability. These results clarify the role of imaginarity of channels in Shor's algorithm and provide a refined perspective on quantum-resource behavior in ideal and noisy sequential quantum algorithms.
发表机构
- Nanchang University（南昌大学）
- Capital Normal University（首都师范大学）
- Max-Planck-Institute for Mathematics in the Sciences（马克斯·普朗克科学促进部数理研究所）
机构由 AI 辅助整理，请以论文原文为准。
